This is the 4436th most frequent Russian word.
внешними
"External" or "outside" (instrumental plural form).
Here, 'внешними' describes the methods as being from outside sources, highlighting their external nature.
Мы решаем проблемы внешними способами.
We solve problems using external methods.
In this sentence, 'внешними' qualifies the partners, indicating they are outside of a certain group or organization.
Она занимается развитием связей с внешними партнерами.
She is engaged in developing relations with external partners.
Here, 'внешними' is used to describe features of nature that are visible or form its outer appearance.